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"You come up with so much more than you would ever think with your tiny little peabrains," she said.

Veep has two more episodes left to film of its upcoming sixth season. The series ended with President Selina Meyer losing the election. So what's next?

"It's an identity crisis for every single character," she teased. "What the heck happens now? It's a lot of Selina trying to figure out what's next and trying to figure out who she is."

Veep also stars Tony Hale, Reid Scott, Timothy Simons, Matt Walsh, Sufe Bradshaw, Kevin Dunn and Gary Cole. The cast was up for the award for Outstanding Performance by an Ensemble in a Comedy Series. Chlumsky said that it's the cast's "favorite" honor.

"We're so gratified by it because it's your peers, people who get what the craft is," she said. "It's hugely gratifying."